Two-swarm PSO for competitive location problems

Abstract

Competitive location problems consist of determining optimal strategies for competing firms which make location decisions. The standard problem is the leader-follower location problem which consists of determining optimal strategies for two competing firms, the leader and the follower, which make decisions sequentially. The follower has the objective of maximizing its market share, given the locations chosen by the leader. The leader optimization problem is to minimize the maximum market share that the follower can get. We propose a two-swarm particle swarm optimization procedure in which each swarm contains locations for one of the two firms. We analyze the application of this procedure to the (r p)-centroid problem in the plane. It is the leader-follower problem where the leader chooses p points and then the follower chooses r points.